Calculating the height of an equilateral triangle - GMAT Quantitative

The area of an equilateral triangle with sidelength is

Using this area for and 20 for in the general triangle formula, we can obtain :

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where is the length of a side and the length of the height.

Therefore, the final answer is .

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is . Therefore:

We derive the height formula from the area of the triangle formula:

The area of an equilateral triangle with sidelength is

Using this area for and 20 for in the general triangle formula, we can obtain :

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where is the length of a side and the length of the height.

Therefore, the final answer is .

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is . Therefore:

We derive the height formula from the area of the triangle formula:

The area of an equilateral triangle with sidelength is

Using this area for and 20 for in the general triangle formula, we can obtain :

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where is the length of a side and the length of the height.

Therefore, the final answer is .

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is . Therefore:

We derive the height formula from the area of the triangle formula:

The area of an equilateral triangle with sidelength is

Using this area for and 20 for in the general triangle formula, we can obtain :

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where is the length of a side and the length of the height.

Therefore, the final answer is .

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is . Therefore: